本书深入浅出地阐述了计算机科学中许多基本而重要的概念，包括布尔逻辑、有限自动机、编程语言、图灵机的普遍性、信息论、算法、并行计算、量子计算、神经网络、机器学习乃至自组织系统。 作者高屋建瓴式的概括，既不失深度，又妙趣横生，相信读者读后会有很多启发。 目录： 序言：石的奇迹 第一章　通用件 第二章　万能积木 第三章　程序设计 第四章　图灵机的普适性 第五章　算法和探索法 第六章　存储：信息与密码 第七章　速度：并行计算机 第八章 自学习与自适应的计算机 第九章　跨越工程设计 致谢

本书全面覆盖线性方程组、矩阵、向量空间、博弈论和数值分析等内容, 理论和应用相结合. 尤其介绍了凸集、对偶定理、赋范[线性]空间、赋范[线性]空间之间的线性映射以及自伴随矩阵本征值的计算等一般教材上没有的内容. 为方便读者学习, 每章都有练习, 并提供解答. 书后还有辛矩阵、洛伦兹群、数值域等16个附录. 本书是一本可供高年级本科生和研究生使用的优秀教材, 同时也是数学教师和相关研究人员的一本很好的参考书.

《概率和鞅》是一部现代概率本科教程,内容生动,叙述严格,主要以离散时间的Doob鞅理论为框架,证明了Kolmogorov强大数定理和三级数理论以及通过运用特征函数的中心极限定理这些重要的结果。概率论作为一门应用学科已经广泛的应用于物理、工程、生物、经济以及社会科学等众多领域。

《有限群的线性表示》是一部非常经典的介绍有限群线性表示的教程，原版曾多次修订重印，作者是当今法国最突出的数学家之一，他对理论数学有全面的了解，尤以著述清晰、明了闻名。《有限群的线性表示》是他写的为数不多的教科书之一，原文是法文(1971年版)，后出了德译本和英译本。《有限群的线性表示》是英译本的重印本。它篇幅不大，但深入浅出的介绍了有限群的线性表示，并给出了在量子化学等方面的应用，便于广大数学、物理、化学工作者初学时阅读和参考。

《哥德尔证明》是第一本既面向学者又面向非专业人士，对哥德尔证明的主要思路和广泛含义作了易读的解释的书。对任何具有逻辑和哲学品味的受过教育的人士来说，它提供了一个深入了解先前无法企及的论题的机会。 在此书的新版中，普利策奖的获奖作者道格拉斯•R·霍夫斯塔特对这一经典著作的原文进行了重新斟酌和更新，澄清了模糊之处，使论述更为清晰，并使行文更具可读性。

希腊数学家阿波罗尼奥斯著。作者与欧几里得、阿基米德常被合称为古希腊亚历山大前期的三大数学家。本书原共8卷，卷Ⅰ～Ⅳ的希腊文本及卷Ⅴ～Ⅶ的阿拉伯文本保存了下来，最后一卷佚失，但其中一些内容的思想方法可以从帕波斯的著作中给出的一些引理中看到。 在阿波罗尼奥斯之前，圆锥曲线的数学性质至迟在公元前4世纪中期即已为希腊人所研究。阿基米德曾不加证明地叙述了圆锥曲线论的一些基本命题。当时，我们今天所谓的抛物线、双曲线和椭圆是用垂直于锥面一母线的平面来割该圆锥所产生的。相应于直角、钝角和锐角圆锥分别就得到抛物线、双曲线和椭圆。但阿波罗尼奥斯采用了截然不同的方法。他只依据同一个圆锥的截面便得到三种圆锥曲线。这种新方法与旧方法相比有许多优点。首先，所有三种曲线都可以用面积贴合的方法来表示，而旧方法只有在抛物线情形才有可能。用现代术语，阿波罗尼奥斯是把三种曲线的方程归于一个坐标系，该坐标系分别以曲线的一已知直径和该直径一端点的切线为坐标轴。它带来了第二种优点：由阿波罗尼奥斯得到曲线的方法立即可进行斜交贴合，而旧方法只允许直交贴合，用现代术语即曲线的坐标可换为任一直径及其切线。正因如此，《圆锥曲线论》开创了对圆锥曲线的现代研究。 该书第Ⅰ卷首先给出了圆锥曲线的定义，在介绍了圆锥曲线的基本性质之后，证明了关于共扼直径的一些简单事实。第Ⅱ卷开头给出了双曲线渐近线的作法和性质，然后引入双曲线的共轭，并证明它与所给双曲线具有相同的渐近线，之后说明如何求一圆锥曲线的直径。第Ⅲ卷论述关于切线与直径所成图形的面积的一些定理，并论述了极点和极线的所谓调和性质。第Ⅳ卷介绍极线的其他性质，讨论了各种位置的圆锥曲线之间可能有的交点的数目，这一点是前人没有论述过的。总之，前4卷除个别内容之外基本上是前人成果的集大成，只是在论述上更加全面和一般。其余几卷则是更加深入的研究。第Ⅴ卷有许多新颖和独特之处，论述了从一特定点到圆锥曲线所能作的最长和最短的线。第Ⅵ卷讲述合同圆锥曲线、相似圆锥曲线及圆锥曲线弓形，指出如何在一给定的直角圆锥上作出与一已知圆锥曲线相等的圆锥曲线。第Ⅶ卷介绍了有心圆锥曲线两共扼直径的性质，并把这些性质与轴的相应性质进行比较。第Ⅷ卷的内容大概是关于怎样求出有心圆锥曲线的直径，使其满足一定条件。 《圆锥曲线论》一书是古代关于圆锥曲线研究的登峰造极之作，它将圆锥曲线的性质网罗殆尽，几乎包括了我们今天所知的关于圆锥曲线的直径、轴、中心、渐近线等的一切性质（虽然它没有提及抛物线的焦点），使得后人几乎没有再研究的余地。在这方面直到17世纪才有所突破，对它的研究大大促进了解析几何学的诞生。

《偏微分方程讲义(第3版)》是俄罗斯科学院院士О.А.奥列尼克多年来在莫斯科大学数学力学系为大学三年级学生讲授该课程基础上的扩充。内容包括偏微分方程理论的古典与现代理论的基础部分，以及泛函分析、广义函数理论、函数空间理论方面的一些知识。作者是И.Г.彼得罗夫斯基的学生，在偏微分方程这个方向享有盛名。此书反映了莫斯科大学在这个课程上，20世纪后半叶至今的新情况，可供我国偏微分方程课教学参考。

本书是俄罗斯著名代数学家A．и．柯斯特利金的优秀教材《代数学引论》的第二卷。《代数学引论》是作者总结了莫斯科大学几十年来代数课程的教学经验而写成的，全书分成三卷(第一卷：基础代数，第二卷：线性代数，第三卷：基本结构)，分别对应于莫斯科大学数学力学系代数教学的三学期的内容。作者在书中把代数、线性代数和几何统一处理成一个教程，并力图把本书写成有利于培养学生创造性思维的教材。书中配置了难度不同的大量习题，并向学生介绍一些专题中尚未解决的问题。. 第二卷的内容包括抽象向量空间的基本概念，双线性型和二次型，线性算子，带有纯量乘积的向量空间，仿射空间与欧几里得点空间，二次曲面，张量。.. 本书可供我国高等院校数学、应用数学专业和相关专业的本科生、研究生、教师用作代数学课程的教学参考书。...

This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.

This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.

This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of Category Theory understandable to this broad readership. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided; a must for computer scientists, logicians and linguists!

This completely updated second edition illustrates the mathematical concepts that a game programmer would need to develop a professional-quality 3D engine. Although the book is geared toward applications in game development, many of the topics appeal to general interests in 3D graphics. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D game programming such as illumination and visibility determination. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series.

The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy student and teacher sewn softcover edition in one volume, with minimal notes and a new index/glossary.

本书用统一的科学概念探讨自然系统和人工系统﹐开创了研究系统的通信和控制的一般规律的新学科﹐它的出版标志着控制论的诞生。它从控制系统的角度揭示了动物和机器﹑生理东西和心理现象的联系﹐为阐明自然界的辩证发展提供了有力的科学证据。它所引起的哲学问题﹐诸如自动机和思维的关系﹑信息的本质等等﹐一直是唯物主义和唯心主义激烈争论的课题。同时﹐控制论也给许多学科提供了一种有力的新方法﹐这种方法已成为沟通各门学科的桥梁。本书所包括的内容十分庞杂，其领域涉及神经生理学、心理学、计算机科学等多学科。20世纪末的新兴理论，如非线性科学、浑沌理论、复杂性理论、人工生命都与控制论的思想有关。控制论应用于工业生产、政治、军事与社会科学的方方面面。事实上，自然科学与社会科学的各学科都广泛地接受并借鉴了控制论的概念。

Review From the reviews: "The book … is a reprinted version of the original English translation of the first volume of B. L. van der Waerden’s ‘Algebra’, without any alterations. However, it is the first softcover printing, worth the price and particularly handy. It is very gratifying to have such an edition … so that further generations of students can both afford it and use it as still one of the best sources … . is one of the most influential textbooks in mathematics of the 20th century." (Werner Kleinert, Zentralblatt MATH, Vol. 1032 (7), 2004) "In the glad to have you back department, I’m delighted that Springer has decided to reprint the two volumes of B.L.van der Waerden’s Algebra. Based in part on lectures by Emmy Noether and Emil Artin, this is the book that brought ‘abstract algebra’ to the mathematical world. … the book reflects the excitement that accompanied the birth of axiomatic algebra. … a book to treasure. I am glad it’s back." (MAA-Online, March, 2004) Product Description This widely known textbook, formally titled Modern Algebra, by the noted Dutch mathematician van der Waerden is now back in print. Algebra originated from notes taken by the author from Emil Artin's lectures. The author extended the scope of these notes to include research of Emmy Noether and her students. The first German edition appeared in 1930-1931, with subsequent editions having been brought up to date. "The basic notions of algebra, groups, rings, modules, fields, and the main theories pertaining to these notions are treated in the classical two volume textbook of van der Waerden. Although more than half a century has elapsed since the appearance of this remarkable book, it is in no way dated, and for the majority of the questions it treats, no better source can be found even today." (I.R. Shafarevich: Encyclopaedia of Mathematical Sciences, Volume 11.1990) Language Notes Text: English (translation) Original Language: German --This text refers to an out of print or unavailable edition of this title. From the Back Cover ...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century. - Saunders MacLane, Notices of the AMS How exciting it must have been to hear Emil Artin and Emmy Noether lecture on algebra in the 1920's, when the axiomatic approach to the subject was amazing and new! Van der Waerden was there, and produced from his notes the classic textbook of the field. To Artin's clarity and Noether's originality he added his extraordinary gift for synthesis. At one time every would-be algebraist had to study this text. Even today, all who work in Algebra owe a tremendous debt to it; they learned from it by second or third hand, if not directly. It is still a first-rate (some would say, the best) source for the great range of material it contains. - David Eisenbud, Mathematical Sciences Research Institute Van der Waerden's book Moderne Algebra, first published in 1930, set the standard for the unified approach to algebraic structures in the twentieth century. It is a classic, still worth reading today. - Robin Hartshorne, University of California, Berkeley --This text refers to an alternate Paperback edition.

《应用随机过程概率模型导论》是一部经典的随机过程著作, 叙述深入浅出、涉及面广，主要内容有随机变量、条件概率及条件期望、离散及连续马尔可夫链、指数分布、泊松过程、布朗运动及平稳过程、更新理论及排队论等；也包括了随机过程在物理、生物、运筹、网络、遗传、经济、保险、金融及可靠性中的应用，特别是有关随机模拟的内容, 给随机系统运行的模拟计算提供了有力的工具。《应用随机过程概率模型导论》有约700道习题, 其中带星号的习题还提供了解答。

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincar Conjecture. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

Aha！Insight（啊哈，灵机一动），ISBN：9787030195869，作者：（美）伽德纳 著，李建臣，刘正新 译

《代数几何原理》主要内容：A third general principle was that this volume should be stir-contained.In particular any "hard" result that would be utilized should be fullyproved. A difficulty a student often faces in a subject as diverse as algebraic geometry is the profusion of cross-references, and this is one reason for attempting to be self-contained. Similarly, we have attempted to avoid allusions to, or statements without proofs of, related results. This book is in no way meant to be a survey of algebraic geometry, but rather is designed to develop a working facility with specific geometric questions.Our approach to the subject is initially analytic: Chapters 0 and 1 treat the basic techniques and results of complex manifold theory, with some emphasis on results applicable to projective varieties. Beginning in Chapter 2 with the theory of Riemann surfaces and algebraic curves, and continu-ing in Chapters 4 and 6 on algebraic surfaces and the quadric line complex, our treatment becomes increasingly geometric along classicallines. Chapters 3 and 5 continue the analytic approach, progressing to more special topics in complex manifolds.